JEE Main 2023 11 April Shift 2 Question Paper with Solution PDF- Download Here

Let a, b, c and d be positive real numbers such that a + b + c + d = 11. If the maximum value of \(a^5b ^3c ^2d\) is \(3750\;\beta\), then the value of \(\beta\) is

• (1) 110
• (2) 90
• (3) 55
• (4) 108

The sum of the coefficients of three consecutive terms in the binomial expansion of (1 + x)ⁿ⁺², which are in the ratio 1 : 3 : 5, is equal to

• (1) 25
• (2) 63
• (3) 92
• (4) 41

If the system of linear equations
7x +11y + αz = 13
5x + 4y + 7z = β
175x + 194y + 57z = 361
has infinitely many solutions, then α + β + 2 is equal to:

• (1) 3
• (2) 4
• (3) 6
• (4) 5

For \(a∈ C, let A = {z∈C : Re (a + z ) > Im ( a + z)}\) and \(B = {z∈C : Re (a + z ) < Im ( a + z)}.\) Then among the two statements: 
(S₁) : If \(Re (a), Im (a) > 0\), then the set A contains all the real numbers 
(S₂): If \(Re (a), Im (a) < 0,\) then the set B contains all the real numbers

• (1) only (S2) is true
• (2) only (S1) is true
• (3) both are true
• (4) both are false

Using all the letters of the word MATHS, then rank of the word THAMS is:

• (1) 101
• (2) 102
• (3) 103
• (4) 104

Let A = {1, 3, 4, 6, 9} and B = {2, 4, 5, 8, 10}. Let R be a relation defined on A × B such that R = {(\((a_1, b_1),(a_2, b_2)\)) : \(a_1 ≤ b_2\) and \(b_1 ≤ a_2\)}. Then the number of elements in the set R is 

• (1) 180
• (2) 26
• (3) 160
• (4) 52

If the \(1011^{th}\) term from the end in the binominal expansion of \((\frac{4x}{5}-\frac{5}{2x})^{2022}\) is 1024 times \(1011^{th}\) term from the beginning, then |x| is equal to

• (1) 10
• (2) 8
• (3) 15
• (4) 12

If \(\begin{vmatrix} x+1 & x & x \\ x & x+ \lambda & x \\ x & x & x+ \lambda^2 \end{vmatrix}\)= \(\frac{9}{8}\) \((103x + 81)\), then \(λ\) and \(\frac{λ}{3}\) are roots of the equation

• (1) 4x² – 24x + 27 = 0
• (2) 4x² – 24x – 27 = 0
• (3) 4x² – 24x + 27 = 0
• (4) 4x² + 24x – 27 = 0

Let mean and variance of the data 1, 2, 4, 5, x, y are 5 and 10 then the mean deviation about mean is?

If f : R \(\rightarrow\) R be a continuous function satisfying \(\int^{\frac{\pi}{2}}_0f(sin2x)sinxdx+\alpha\int^{\frac{\pi}{4}}_0f(cos2x)cosxdx=0\), then the value of \(\alpha\) is

• (1) -√3
• (2) √3
• (3) -√2
• (4) √2

Let f and g be two function defined by \(f(x) =   \begin{cases}     x+1       & \quad x<0\\    |x-1|,   & \quad x \geq0   \end{cases}\) and g(x) = \(f(n) =   \begin{cases}     x+1,       & \quad x<0 \\     1,  & \quad x\geq0   \end{cases}\) Then (gof)(x) is 

• (1) Continuous everywhere but not differentiable at x = 1
• (2) Continuous everywhere but not differentiable exactly at one point
• (3) not continuous at x = – 1
• (4) differentiable everywhere

\(\frac{dy}{dx}\) + \(\frac{5}{x(1+x^5)}\)y = \(\frac{(1+x^5)^2}{x^7}\) If y(1) = 2, then the value of y(2) is:

• (1) \(\frac{693}{128}\)
• (2) \(\frac{697}{128}\)
• (3) \(\frac{637}{128}\)
• (4) \(\frac{627}{128}\)

Let the function f: [0,2] \(\rightarrow\) R be defined as \(f(x) =   \begin{cases}     e^{min}{x^2,x-[x]}       & \quad x \in[0,1]\\     e^{[x-log_ex]}  & \quad x\in[1,2]   \end{cases}\)
where [t] denotes the greatest integer less than or equal to t. Then the value of the integral \(\int^2_0xf(x)dx\) is 

• (1) \(\bigg(e^2+\frac{1}{2}\bigg)\)
• (2) 2e-1
• (3) \(1+\frac{3e}{2}\)
• (4) \(2e-\frac{1}{2}\)

The domain of the function f(x) = \(\frac{1}{\sqrt{[x]^2-3[x]-10}}\) is (where [x] denotes the greatest integer less than or equal to x)

• (1) (-∞,-2) ∪ (6, ∞)
• (2) (-∞,-2) ∪ (5, ∞)
• (3) (-∞,-3) ∪ (6, ∞)
• (4) (-∞,-3) ∪ (5, ∞)

If the radius of the largest circle with centre (2, 0) inscribed in the ellipse \(x^2 + 4y^2 = 36\) is r, then \(12r^2\) is equal to

• (1) 92
• (2) 69
• (3) 72
• (4) 115

The converse of ((~ p) ∧ q) ⇒ r is

• (1) r ⇒ (p v ~q)
• (2) ~r ⇒ (~p ∧ q)
• (3) ~r ⇒ (p v ~q)
• (4) r ⇒ (~p ∧ q)

If four distinct points with position vectors \(\overrightarrow a,\overrightarrow b,\overrightarrow c\)  and \(\overrightarrow d\)  are coplanar, then \([\overrightarrow a \overrightarrow b \overrightarrow c]\) is equal to

• (1) \([\overrightarrow a \overrightarrow d \overrightarrow b]+[\overrightarrow d \overrightarrow c \overrightarrow a]+[\overrightarrow d\overrightarrow b\overrightarrow c] \)
• (2) \([\overrightarrow b \overrightarrow c \overrightarrow d]+[\overrightarrow d \overrightarrow a \overrightarrow c]+[\overrightarrow d\overrightarrow b\overrightarrow a]\)
• (3) \([\overrightarrow d \overrightarrow b \overrightarrow a]+[\overrightarrow a \overrightarrow c \overrightarrow c]+[\overrightarrow d\overrightarrow b\overrightarrow c]\)
• (4) \([\overrightarrow d \overrightarrow c \overrightarrow a]+[\overrightarrow b \overrightarrow d \overrightarrow a]+[\overrightarrow c\overrightarrow d\overrightarrow b]\)

Let the line passing through the points P (2, –1, 2) and Q (5, 3, 4) meet the plane x – y + z = 4 at the point R. Then the distance of the point R from the plane x + 2y + 3z + 2 = 0 measured parallel to the line \(\frac{x-7}{2}=\frac{y+3}{2}=\frac{z-2}{1}\) is equal to

• (1) \(\sqrt{189}\)
• (2) \(\sqrt{31}\)
• (3) \(\sqrt{61}\)
• (4) 3

Let P be the plane passing through the points (5, 3, 0), (13, 3, –2) and (1, 6, 2). For α ∈ N, if the distances of the points A (3, 4, α) and B (2, α, a) from the plane P are 2 and 3 respectively, then the positive value of a is

• (1) 5
• (2) 6
• (3) 3
• (4) 4

The angle of elevation of the top P of a tower from the feet of one person standing due South of the tower is 45° and from the feet of another person standing due west of the tower is 30°. If the height of the tower is 5 meters, then the distance (in meters) between the two persons is equal to

• (1) \(\frac{5}{2}\sqrt5\)
• (2) 10
• (3) 5
• (4) \(5\sqrt5\)

Let \(\overrightarrow a=\overrightarrow i+2\overrightarrow j+3 \overrightarrow k\) and \(\overrightarrow b= \overrightarrow i+ \overrightarrow j - \overrightarrow k\) . If \(\overrightarrow c\) is a vector such that \(\overrightarrow a. \overrightarrow c=11,\overrightarrow b.(\overrightarrow a.\overrightarrow c)=27\) and \(\overrightarrow b. \overrightarrow c=-\sqrt{3}|b|,\)  then \(|\overrightarrow a \times \overrightarrow c|^2\) is equal to _______ .

Let A = {1, 2, 3, 4, 5} and B = {1, 2, 3, 4, 5, 6). Then the number of functions f: A→B satisfying f(1) + f(2) = f(4)-1 is equal to _________ .

Let the probability of getting head for a biased coin be \(\frac{1}{4}\) . It is tossed repeatedly until a head appears. Let N be the number of tosses required. If the probability that the equation \(64x² + 5Nx + 1 = 0\) has no real root is \(\frac{p}{q}\) , where p and q are co-prime, then q – p is equal to _______.

If A is the area in the first quadrant enclosed by the curve \(C: 2x^2 – y + 1 = 0\), the tangent to C at the point (1, 3) and the line x + y = 1, then the value of 60A is ________

Let S = \(\{z \in C-\{i,2i\}:\frac{z^2+8iz-15}{z^2-3iz-2}\in R\}\) if \(\alpha-\frac{13}{11}i\in S, a \in R-{0}\), then  \(242\alpha^2\) is equal to ____.

The number of points, where the curve \(f(x) = e^{8x} - e^{6x} - 3e^{4x} - e^{2x} + 1\), \(x ∈ R\) cuts x-axis, is equal to

Let the line / : x = \(\frac{1-y}{2}=\frac{z-3}{\lambda}, \lambda \in R\) meet the plane P : x+2y +3z = 4 at the point \((\alpha, \beta, \lambda)\). If the angle between the line I and the plane P is \(cos^{-1}\bigg(\sqrt{\frac{5}{14}}\bigg)\) then \(\alpha+2\beta+6\lambda\) is equal to______.

For \(k ∈ N\), if the sum of the series \(1 + \frac{4}{k}+\frac{8}{k^2}+\frac{13}{k^3}+\frac{19}{k^4}+..\)..  is 10, then the value of k is___

Let the tangent to the parabola \(y^2 = 12x\) at the point (3, α) be perpendicular to the line 2x + 2y = 3. Then the square of distance of the point (6, – 4) from the normal to the hyperbola \(α^2 x^2 – 9y^2 = 9α^2\) at its point (α– 1, α + 2) is equal to__

If the line \(l_1 : 3y - 2x = 3\) is the angular bisector of the lines \(l_2 : x - y + 1 = 0\) and \(l_3\) : \(αx + βy + 17 = 0\), then \(α^2 + β^2  - α - β\) is equal to__

The current flowing through \(R_2\) is

• (1) \(\frac{1}{3}A\)
• (2) \(\frac{1}{2}A\)
• (3) \(\frac{2}{3}A\)
• (4) \(\frac{1}{4}A\)

A plane electromagnetic wave of frequency 20 MHz propagates in free space along x-direction. At a particular space and time, \(\overrightarrow E =6.6 \;\hat jV/m  .\)What is \(\overrightarrow B\) at this point ?

• (1) \(-2.2 \times 10^{-}\hat i\;T \)
• (2) \(-2.2 \times 10^{-8}\hat k\;T\)
• (3) \(2.2 \times 10^{-8}\hat i\;T\)
• (4) \(2.2 \times 10^{-8}\hat k\;T\)

An electron is allowed to move with constant velocity along the axis of current carrying straight solenoid.
A. The electron will experience magnetic force along the axis of the solenoid. 
B. The electron will not experience magnetic force. 
C. The electron will continue to move along the axis of the solenoid. 
D. The electron will be accelerated along the axis of the solenoid. 
E. The electron will follow parabolic path-inside the solenoid. 
Choose the correct answer from the options given below :

• (1) A and D only
• (2) B, C and D only
• (3) B and C only
• (4) B and E only

In which of the following process, the internal energy of gas remains constant

• (1) Isothermal
• (2) Isochoric
• (3) Isobaric
• (4) Adiabatic

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R
Assertion (A): A bar magnet dropped through a metallic cylindrical pipe takes more time to come down compared to a non-magnetic bar with same geometry and mass. 
Reason (R) : For the magnetic bar, Eddy currents are produced in the metallic pipe which oppose the motion of the magnetic bar. 
In the light of the above statement, choose the correct answer from the options given below : 

• (1) Both A and R are true and R is the correct explanation of A
• (2) A is false but R is true
• (3) Both A and R are true but R is NOT the correct explanation of A
• (4) A is true but R is false

The energy of \(He^+\) ion in its first excited state is, (The ground state energy for the Hydrogen atom is – 13.6 eV) :

• (1) -13.6 eV
• (2) -3.4 eV
• (3) -54.4 eV
• (4) -27.2 eV

When one light ray is reflected from a plane mirror with 30° angle of reflection, the angle of deviation of the ray after reflection is :

• (1) 140°
• (2) 110°
• (3) 120°
• (4) 130°

A capacitor of capacitance C is charged to a potential V. The flux of the electric field through a closed surface enclosing the positive plate of the capacitor is :

• (1) \(\frac{CV}{2\epsilon_0}\)
• (2) \(\frac{2CV}{\epsilon_0}\)
• (3) Zero
• (4) \(\frac{CV}{\epsilon_0}\)

Proton and electron have equal kinetic energy, the ratio of de-Broglie wavelength of proton and electron is \(\frac{1}{x}\). Find x. (Mass of proton 1849 times mass of electron)

Eight equal drops of water are falling through air with a steady speed of 10 cm/s. If the drops coalesce, the new velocity is :

• (1) 5 cm/s
• (2) 40 cm/s
• (3) 16 cm/s
• (4) 10 cm/s

The logic operations performed by the given digital circuit is equivalent to:

• (1) NAND
• (2) NOR
• (3) OR
• (4) AND

A particle is projected at an angle of 30° with ground with speed 40 m/s. The speed of the particle after 2 s is (use g=10 ms^-2)

A body of mass 500 g moves along x-axis such that it's velocity varies with displacements x according to the relation \(v  =10 \sqrt x\) m/s the force acting on the body is :

• (1) 25 N
• (2) 125 N
• (3) 5 N
• (4) 166 N

A space ship of mass 2 × 10⁴ kg is launched into a circular orbit close to the earth surface. The additional velocity to be imparted to the spaceship in the orbit to overcome the gravitational pull will be (if g = 10 m/s² and radius of earth = 6400 km)

• (1) 11.2 (√2 -1) km/s
• (2) 7.9 (√2 - 1) km/s
• (3) 8(√2 -1) km/s
• (4) 7.4(√2 - 1) km/s

When vector \(\overrightarrow A = 2\hat i+3\hat J+2\hat k\) is subtracted from vector \(\overrightarrow B\)  , it gives a vector equal to \(2\hat j\) . Then the magnitude of vector \(\overrightarrow B\) will be :

• (1) √6
• (2) √5
• (3) 3
• (4) √13

If force (F), velocity (V) and time (T) are considered as fundamental physical quantity, then dimensional formula of density will be :

• (1) \(F^2V^{–2}T^6\)
• (2) \(FV^4T^{–6}\)
• (3) \(FV^{–2}T^2\)
• (4) \(FV^–4T^{–2}\)

Potential at the surface of a uniformly charged non-conducting sphere is V. Then the potential at its centre is

• (1) 0
• (2) \(\frac{V}{2}\)
• (3) \(2V\)
• (4) \(\frac{3V}{2}\)

The root mean square speed of molecules of nitrogen gas at 27°C is approximately : (Given mass of a nitrogen molecule = \(4.6 × 10^{–26}\) kg and take Boltzmann constant KB = \(1.4 × 10^{–23}\) JK–1 )

• (1) 1260 m/s
• (2) 91 m/s
• (3) 27.4 m/s
• (4) 523 m/s

A car P travelling at 20 \(ms^{–1}\) sounds its horn at a frequency of 400 Hz. Another car Q is travelling being the first car in the same direction with a velocity 40 \(ms^{–1}\) . The frequency heard by the passenger of the car Q is approximately [Take, velocity of sound = 360 \(ms^{–1}\) ]

• (1) 485 Hz
• (2) 421 Hz
• (3) 471 Hz
• (4) 514 Hz

In satellite communication, the uplink frequency band used is :

• (1) 76 – 88 MHz
• (2) 3.7 – 4.2 GHz
• (3) 5.925 – 6.425 GHz
• (4) 420 – 890 MHz

As shown in the figure, a plane mirror is fixed at a height of 50 cm from the bottom of tank containing water (μ = 4/3). The height of water is the tank is 8 cm. A small bulb is placed at the bottom of the water tank. The distance of image of the bulb formed by mirror from the bottom of the tank is ____cm.

A circular plate is rotating in horizontal plane, about an axis passing through its center and perpendicular to the plate, with an angular velocity ω . A person sits at the center having two dumbbells in his hands. When he stretches out his hands, the moment of inertia of the system becomes triple. If E be the initial Kinetic energy of the system, then final Kinetic energy will be E/x. The value of x is

The surface tension of soap solution is 3.5 × 10–2 Nm–1. The amount of work done required to increase the radius of soap bubble from 10 cm to 20 cm is________× 10–4 J. (take π = 22/7)

A wire of density \(8 × 10^3\) \(kg/m^3\) is stretched between two clamps 0.5 m apart. The extension developed in the wire is \(3.2 × 10^{–4}\) m. If Y = \(8 × 10^{10}\) \(N/m^2\) , the fundamental frequency of vibration in the wire will be ________Hz.

A metallic cube of side 15 cm moving along y-axis at a uniform velocity of 2 ms^–1. In a region of uniform magnetic field of magnitude 0.5T directed along z-axis. In equilibrium the potential difference between the faces of higher and lower potential developed because of the motion through the field will be ___ mV.

A nucleus disintegrates into two nuclear parts, in such a way that ratio of their nuclear sizes is \(1 : 2^{2/3}\) . Their respective speed have a ratio of n : 1. The value of n is _______.

A block of mass 5 kg starting from rest pulled up on a smooth incline plane making an angle of 30^◦ with horizontal with an affective acceleration of 1 ms⁻². The power delivered by the pulling force at t = 10 s from the starts is W. [use g=10 ms⁻²] (Calculate the nearest integer value)

In the given circuit \(C_1 = 2μF, C_2 = 0.2μF, C_3 = 2μF, C_4 = 4μF, C_5 = 2μF, C_6 = 2μF\). The charge stored on capacitor \(C_4\) is _____ \(μC\)

A coil has an inductance of 2H and resistance of 4W, A 10V is applied across the coil. The energy stored in the magnetic field after the current has built up to its equilibrium value will be ____ × 10^{–2} J.

Two identical cells each of emf 1.5 V are connected in series across a 10Ω resistance. An ideal voltmeter connected across 10 resistance reads 1.5 V. The internal resistance of each cell is ______Ω.

Which one of the following pairs is an example of polar molecular solids ?

• (1) HCl (s), AlN (s) 
• (2) MgO (s), SO₂(s)
• (3) SO₂(s), NH₃(s)
• (4) SO₂(s), CO₂(s)

The major product formed in the following reaction is
 
A.
B.
C.
D.
Choose the correct answer from the options given below:

• (1) C only
• (2) A only
• (3) D only
• (4) B only

Compound ‘B’ is

• (1)

• (2)

• (3)

• (4)

Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: [CoCl(NH₃)]^2– absorbs at lower wavelength of light with respect to [Co(NH₃)₅(H₂O) ^3–
Reason R: It is because the wavelength of the light absorbed depends on the oxidation state of the metal ion.
In the light of the above statements, choose the correct answer from the options given below:

• (1) Both A and R are true and R is the correct explanation of A 
• (2) A is true but R is false 
• (3) Both A and R are true but R is NOT the correct explanation of A
• (4) A is false but R is true

If Ni^2– is replaced by Pt^2– in the complex NiCl₂Br₂] ^2– , which of the following properties are expected to get changed?
A. Geometry
B. Geometrical isomerism
C. Optical isomerism
D. Magnetic properties

• (1) A, B and C
• (2) B and D
• (3) B and C
• (4) A, B and D

Given below are two statements. one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : A solution of the product obtained by heating a mole of glycine with a mole of chlorine in presence of red phosphorous generates chiral carbon atom.
Reason R : A molecule with 2 chiral carbons is always optically active.
In the light of the above statements, choose the correct answer from the options given below:

• (1) A is true but R is false
• (2) Both A and R are true but R is NOT the correct explanation of A
• (3) Both A and R are true and R is the correct explanation of A
• (4) A is false but R is true

• (1) A-II, B-IV, C-I, D-III
• (2) A-II, B-III, C-l, D-IV
• (3) A-III, B-IV, C-II, D-I
• (4) A-II, B-III, C-IV, D-I

What weight of glucose must be dissolved in 100 g of water to lower the vapour pressure by 0.20 mm Hg?
(Assume dilute solution is being formed)
Given : Vapour pressure of pure water is 54.2 mm Hg at room temperature. Molar mass of glucose is 180 g mol^–1 .

• (1) 4.69 g
• (2) 2.59 g
• (3) 3.59 g
• (4) 3.69 g

A solution is prepared by adding 2 g of X” to 1 moIe of water. Mass percent of “X” in the solution is

• (1) 20%
• (2) 5%
• (3) 10%
• (4) 2%

Compound from the following that will not produce precipitate on reaction with Compound from the following that will not produce precipitate on reaction with AgNO₃ is:

• (1)

• (2)

• (3)

• (4)

The magnetic moment is measured in Bohr Magneton (BM).
Spin only magnetic moment of Fe in [Fe(H₂O)₆] ³⁺ and [Fe(CN)₆] ^3– complexes respectively is:

• (1) 5.92 B.M. and 1.732 B.M
• (2) 6.92 B.M. in both
• (3) 3.87 B.M. and 1.732 B.M.
• (4) 4.89 B.M. and 6.92 B.M.

Given below are two statements. one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: can be subjected to Wolff-Kishner reduction to give
Reason R: Wolff-Kishner reduction is used to convert into 
In the light of the above statements, choose the correct answer from the options given below:

• (1) A is true but R is false
• (2) ) Both A and R are true and R is the correct explanation of A
• (3) A is false but R is true
• (4) Both A and R are true but R is NOT the correct explanation of A

• (1) 80 and 4
• (2) 160 and 4
• (3) 40 and 4
• (4) 80 and 2

Product [X] formed in the above reaction is:

• (1)

• (2) H₃C-CH₂-CH=CH₂
• (3) H₃C-CH=CH-CH₃
• (4)

Alkali metal from the following with least melting point is:

• (1) Rb
• (2) Na
• (3) K
• (4) Cs

Given below arc two statements:
Statement I : In the metallurgy process. sulphide ore is converted to oxide before reduction.
Statement II : Oxide ores in general are easier to reduce.
In the light of the above statements, choose the most appropriate answer from the options given below

• (1) Both Statement I and Statement II are correct
• (2) Statement I is correct but Statement II is incorrect
• (3) Statement I is incorrect but Statement II is correct
• (4) Both Statement I and Statement II are incorrect

Which of the following compounds is an example of Freon?

• (1) C₂Cl₂F₂
• (2) C₂HF₃
• (3) C₂F₄
• (4) C₂H₂F₂

Which hydride among the following is less stable?

• (1) HF
• (2) BeH₂
• (3) NH₃
• (4) LiH

Given below are two statements:
Statement I : Ethene at 333 to 343 K and 6-7 atm pressure in the presence of AIEt₃ and TiCl₄ undergoes addition polymerization to give LDP.
Statement II: Caprolactam at 533-543 K in H₂O through step growth polymerizes to give Nylon 6.
In the light of the above statements, choose the correct answer from the options given below:

• (1) Both Statement t and Statement II are false
• (2) Statement I is true but Statement II is false
• (3) Both Statement I and Statement II are true
• (4) Statement I is false but Statement II is true

One mole of P₄ reacts with 8 moles of SOCI₂ to give 4 moles of A. x mole of SO₂ and 2 moles of B. A, B and x respectively are

• (1) POCl₃, S₂Cl₂ and 4
• (2) PCl₃, S₂Cl₂ and 2
• (3) PCi₃, S₂Cl₂ and 4
• (4) POCl₃, S₂Cl₂ and 2

The number of possible isomeric products formed when 3-chioro-1-butene reacts with HCl through carbocation formation is __________

The maximum number of lone pairs of electron on the central atom from the following species is ___________
ClO₃^– , XeF₄, SF₄ and I₃^–

The total number of intensive properties from the following is __________
Volume. Molar heat capacity, Molarity, E^θ cell. Gibbs free energy change. Molar mass, Mole

Number of compounds from the following which will not produce orange red precipitate with Benedict solution is ____________
Glucose, maltose, sucrose, ribose, 2-deoxyribose, amylose, lactose

The number of correct statement from the following is _________ .
A. For 1s orbital, the probability density is maximum at the nucleus
B. For 2s orbital, the probability density first increases to maximum and then decreases sharply to zero.
C. Boundary surface diagram of the orbitals encloses a region of 100% probability of finding the electron.
D. p and d-orbitals have 1 and 2 angular nodes respectively E. probability density of p-orbital is zero at the nucleus

4.5 moles each of hydrogen and iodine is heated in a sealed ten litre vessel. At equilibrium, 3 moles of HI were found. The equilibrium constant for H₂(g) + I₂(g) ⇋ 2HI(g) is _____________ .

The number of correct statements from the following is ______
A. E^cell is an intensive parameter
B. A negative E^θ means that the redox couple is a stronger reducing agent than the H^– H₂ couple.
C. The amount of electricity required for oxidation or reduction depends on the stoichiometry of the electrode reaction.
D. The amount of chemical reaction which occurs at any electrode during electrolysis by a current is proportional to the quantity of electricity passed through the electrolyte.

The volume of hydrogen liberated at STP by treating 2.4 g of magnesium with excess of hydrochloric acid is _________ × 10^–2 L
Given : Molar volume of gas is 22.4 L at STP.
Molar mass of magnesium is 24 g mol^–1

The number of correct statements about modern adsorption theory of heterogeneous catalysis from the following is _______
A. The catalyst is diffused over the surface of reactants.
B. Reactants are adsorbed on the surface of the catalyst.
C. Occurrence of chemical reaction on the catalysts surface through formation of an intermediate.
D. It is a combination of intermediate compound formation theory and the old adsorption theory
E. It explains the action of the catalyst as well as those of catalytic promoters and poisons.

Mg(NO₃)₂. XH₂O and Ba(NO₃)₂.YH₂O, represent formula of the crystalline forms of nitrate salts. Sum of X and Y is _____________ .